Did Feynman make a mistake in the drawing of moving charges?

[Jaaanosik]

TL;DR Summary

Did Feynman make a mistake in the drawing of moving charges?

This is from Feynman's lectures: https://www.feynmanlectures.caltech.edu/II_26.html

Should the (b) say F1=q1E2 and F2=q2E1?

 

[DrClaude]

It is an arbitrary choice. I take it that ##\mathbf{E}_1## and ##\mathbf{B}_1## are the electric and magnetic field at the position of particle 1.

 

[Jaaanosik]

It is an arbitrary choice. I take it that ##\mathbf{E}_1## and ##\mathbf{B}_1## are the electric and magnetic field at the position of particle 1.

That does not make sense.
If there is a charge ##q_3## and the field from ##q_2## would be named ##\mathbf{E}_3##?

This is more intuitive: source...

 

[Orodruin]

That does not make sense.
If there is a charge ##q_3## and the field from ##q_2## would be named ##\mathbf{E}_3##?

This is more intuitive: source...

View attachment 345367

That’s completely subjective. There is nothing wrong with naming the fields at 1 ##\vec E_1## and ##\vec B_1##, respectively. In the end, there is only a single electromagnetic field so in some sense it is more natural to use that naming convention. The only reason you can split the field into contributions from different sources is that Maxwell’s equations are linear. This is not the case for all field theories.

 

[Dale]

As long as the diagrams match the text and the equations then it is not a mistake. But it certainly could be confusing even without being a mistake

 

[codelieb]

First of all, I would like to mention that Feynman did not draw this figure. Matthew Sands drew it. Feynman's figure we much simpler; You can see him standing by it in photo #9 of the blackboard photos that are posted with this lecture in the online edition of FLP. Secondly, it seems obvious that in this figure E_n and B_n are the electric and magnetic field at charge q_n. I see nothing confusing about this whatsoever.

 

[Drakkith]

Should the (b) say F1=q1E2 and F2=q2E1?

No, the diagram is clearly labeled, showing that E1 points left from q1 (the left arrow labeled q1E1), while the right arrow from q2 is labeled q2E2.

That does not make sense.
If there is a charge ##q_3## and the field from ##q_2## would be named ##\mathbf{E}_3##?

That is certainly a valid option for labeling diagrams. But note that it's not "the field from q2", it's "the field at q3".

This is more intuitive: source...

Not really. That source is talking about placing a test charge in a field produced by 2+ charges (for a total of 3+ charges), whereas your post is about the force of a single charge acting on a single other charge. Note that you are NOT drawing field lines from each charge in your first post (or decomposing the composite lines into their individual charge contributions), which is what they do in the diagram you linked in post #3.

The line labeled q1E1 in the first post isn't a field line, it's the electric force on the particle. Same for the q2E2 line.